Circular and Satellite Motion Legacy Problem #16 Guided Solution
Problem*
Tyrone and Mia have masses of 84 kg and 59 kg respectively. They sit 1.0 m apart in the front center of Mr. H's Physics class. For some time, they each have been sensing a sort of electricity in their growing relationship. And now, six units into their Physics course, they have learned that they are gravitationally attracted to each other. Determine the magnitude of this force of gravitational attraction.
Audio Guided Solution
Newton's Law of Universal Gravitation states that all objects with mass attract each other with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance which separates them. The equation which expresses this relationship is that f-graph equals big G times m times n divided by the distance of separation, square. Applied to Tyrone and Mio, what we would do is we would calculate f-graph by taking the big G value, which is known as the universal gravitation constant, and has a numerical value of 6.673 times 10 to the negative 11th Newton's meter squared per kilogram squared. We take that proportionality constant, we multiply it by the mass of Tyrone, 84 kilograms, times the mass of Mio, 59 kilograms, and we would divide by the distance of separation, square, that is 1 meter squared. When we do that, we find that Tyrone and Mio have a disappointing sort of traction that is only 3.307 times 10 to the negative 7th Newton.
Solution
3.3 x 10-7 N
Habbits of an Effective Problem Solver
- Read the problem carefully and develop a mental picture of the physical situation. If necessary, sketch a simple diagram of the physical situation to help you visualize it.
- Identify the known and unknown quantities in an organized manner. Equate given values to the symbols used to represent the corresponding quantity - e.g., \(\descriptive{m}{m,mass} = 61.7\unit{kg}\), \(\descriptive{v}{v,velocity} = 18.5 \unit{\meter\per\second}\), \(\descriptive{R}{R,radius} = 30.9\unit{m}\), \(F_\text{norm} = \colorbox{gray}{Unknown}\).
- Use physics formulas and conceptual reasoning to plot a strategy for solving for the unknown quantity.
- Identify the appropriate formula(s) to use.
- Perform substitutions and algebraic manipulations in order to solve for the unknown quantity.
Read About It!
Get more information on the topic of Circular and Satellite Motion at The Physics Classroom Tutorial.